Abstract

We consider the problem of optimal scaling of the proposal variance
for multidimensional Random walk Metropolis (RWM) algorithms. It is
well known, for a wide range of continuous target densities, that
the optimal scaling of the proposal variance leads to an average
acceptance rate of 0.234. Therefore a natural question is, do
similar results for target densities which have discontinuities? In
the current work, we answer in the affirmative for a class of
spherically constrained target densities. Even though the acceptance
probability is more complicated than for continuous target
densities, the optimal scaling of the proposal variance again leads
to an average acceptance rate of 0.234.